Plasma Weapons

What are Plasma Weapons?

Plasma weapons are one of the most popular ideas in sci-fi.
Babylon5 uses something called "PPGs", which stands for
Phased Plasma Guns. No one knows exactly what's "phased"
about it, since a plasmoid is a highly randomized entity, but
"phased" is ultimately just another one of those science
terms that's become almost meaningless thanks to gratuitous sci-fi
abuse. In any case, PPG blasts look like glowing dots and move at
markedly subsonic speeds. Similarly, the Romulans used a "plasma
torpedo" in the classic Star Trek episode "Balance of
Terror". It looked like a large glowing orange blob. And
finally, a considerable number of Star Wars fans (perhaps influenced
by Star Trek) have jumped on the bandwagon and decided that the
green-hued turbolaser bolts of Star Wars are plasma weapons too.

A Babylon-5
crewman fires his PPG at a VorlonFrom "Falling Toward
Apotheosis"

The Romulan
plasma torpedoFrom the classic episode "Balance of
Terror"

But what, exactly, are plasma weapons? For those who are not
already aware, plasma is usually described as the fourth state of
matter, after solid, liquid, and gas. More technically, it is ionized
gas, ie- gas in which the energy level is so high that the electrons
will not stay confined in their atomic energy shells so they escape.
The Earth's Sun is largely composed of plasma, which can also be
described as a hot "soup" of free-floating nuclei and
electrons. Therefore, a plasma weapon would logically be
something that fires plasma at the target.

However, particle beams fire ions at the target, yet they are
generally called particle beams, not "plasma weapons". So
what is the distinction? It seems to be that a plasma weapon is
primarily a heat-based weapon, ie- it is the internal energy of a hot
plasmoid which damages the target, not the forward kinetic energy of
the ion stream.

Indeed, so-called "plasma weapons" in sci-fi generally
fire visible "bolts" which move far, far slower than the
particles of a hot plasma would move. For example, a typical
hand-held "plasma weapon" in sci-fi will fire a bolt that
moves at 1 km/s at the most, or may even be subsonic, yet even a
relatively "cold" 1 eV plasma will have an average (root
mean squared) particle velocity of 13.8 km/s for nuclei and 593 km/s
for electrons (assuming even energy distribution). This is a major
impediment to their effectiveness and an incomprehensible "feature";
why would one even want a plasma weapon where the particle
velocities are all randomized in a slow-moving confined blob, rather
than being directed forward at great velocity as they would be in a
particle beam? Such a weapon would be far less penetrative by its
nature, hence far less efficient even if it works.

And these weapons generally have one other fascinating on-screen
trait: they do not appear to be affected by gravity. This is not a
small quibble; dense objects like bullets drop in gravity, and light
objects like helium balloon float up due to buoyancy. You can't
normally see a bullet dropping because it is too small and fast to
see with the naked eye in flight, but the arcing is appreciable and
significant, yet it is not present in sci-fi "plasma weapon"
blasts, which fly straight and true to their targets as if there is
no gravity at all. One could attempt to rationalize this with a
projectile that has the density of air, but if it has the density of
air, then it would have the aerodynamic properties of a cool air
balloon, which would make a poor projectile to say the least.

How well would a Plasma Weapon work?

The short answer is: at any range where it takes more than a
thousandth of a second for the bolt to reach the target, not too
well. You see, plasma spreads very quickly, and while plasma guns
actually do exist in real-life1,
and have been proposed as a mechanism for replenishing the fuel
burn-up fraction in a Tokomak-style fusion reactor for steady-state
operation, they have never been seriously considered as a weapon.
They can fire a "blob" of plasma in the MJ-range, but this
blob would not stay together for much distance in vacuum, never mind
atmosphere where they would run into a virtual brick wall (sea-level
atmosphere is billions of times denser than a fusion plasma). You
could extend the range by hurling these ions out of the barrel at an
extreme velocity (eg- relativistic), but those moving bolts we see in
sci-fi do not appear to be traveling anywhere near that
quickly.

All right, so why don't we just confine the plasma? Well of
course, there's the obvious objection that a blob of plasma will not
confine itself, so you'd have to create some kind of magical
containment field which moves with the bolt and requires no
technological apparatus to sustain itself. But it gets worse. Let's
say we're talking about a 1 metre long bolt with a diameter of ½
cm, and a yield of 1 MJ (equivalent to roughly 4 ounces of TNT).
Let's say it's 1 keV plasma (roughly 8 million K); you would need
6.24E21 ions, ie- less than 0.01 grams of hydrogen plasma. Small
problem: air would be many times denser then this plasma, so the bolt
would tend to fly up because of buoyancy, and it would need
some kind of propulsion system to drive it through air because it
certainly isn't going to coast through atmospheric resistance on its
miniscule momentum. Both of these problems can be alleviated through
sheer particle velocity (a sufficiently hypersonic projectile will
have enough momentum to mitigate buoyancy effects and extend its
range). But since that would be more of a particle beam than a sci-fi
moving-blob "plasma weapon", it is not applicable here. In
short, a typical subsonic or marginally supersonic sci-fi moving-blob
plasma blast would require a magical self-contained containment
field, and it would float up into the air even if it did hold
together.

In short, ask yourself how well a "hot steam gun" would
work. Doesn't sound all that impressive, does it? You visualize a
cloud of steam shooting out of a gun and promptly dissipating in the
air. So why does it sound like such a great idea when you replace
"steam" with "plasma", which is just a really hot
gas?

Can you make a Plasma Weapon work?

OK, why don't we try solving this problem by using a much
lower-energy plasma with increased density? We could try to solve the
buoyancy problem by making it colder (say, 1 eV, or 8000K, which is a
bit hotter than the surface of the Sun), thus necessitating a
thousand times more ions in the same volume, but its density would
still be much too low to push it through the atmosphere on
momentum alone. It wouldn't necessarily float up, but try throwing a
balloon at someone and you can see how well an object with
atmospheric density would fly if hurled at the target.

No, if you want it to push its way through atmosphere on momentum,
it must be either much denser than air or moving at extreme velocity,
which sci-fi plasma weapons generally do not (and which would make it
more of a particle beam than a traditional sci-fi "plasma
weapon"). So what if we decrease the volume to make it as dense
as a solid projectile? Well, that takes care of the "can't push
its way through atmosphere" problem, but now you have to make it
tiny, and in order to do that, you need to squeeze it with immense
pressure. If we squeeze our 1MJ plasmoid into a 1cc volume and apply
the ideal gas law (which is a good model for plasmas), we find that
the pressure is in the range of 700 GPa! When you consider the
fact that this is a thousand times greater than the yield strength
of high-grade steel, you can begin to see the problem.

How many problems arise when you need a containment field a
thousand times stronger than steel just to hold your plasmoid
together? Some questions leap to mind, such as "if they can
create such a strong containment field which somehow supports itself
and doesn't even need a projector device, then why can't they make
personal shields as strong or even stronger?" One would also
have to ask why it doesn't glow like the Sun, since it would be
hotter than the Sun's photosphere and denser than steel. And finally,
one would have to ask what the point is of this whole speculation,
since our plasma "bullet" is now denser than aluminum and
should act like a real bullet now, which means it should drop in
gravity. While that may not be an insurmountable hurdle for a
hypothetical sci-fi weapon, it certainly doesn't match the sci-fi
weapons we know, which do not arc noticeably in gravity.

In conclusion, the idea of a slowly moving self-contained plasmoid
weapon simply doesn't make any sense. Your "bolt" is
constantly trying to blow itself apart on the way to the target, you
must invent some kind of ridiculously strong yet easy-to-run
containment field to make it hold together (thus raising obvious
questions about why this super containment technology is not used to
effortlessly protect against these bolts), and when it finally
does hit the target and the mythical "containment field"
shatters, the barely-contained ions within will promptly scatter in
all directions, thus wasting the majority of their energy by
dissipating harmlessly into space. Even those ions that do
strike the surface of the target will achieve poor penetration; most
of their kinetic energy is randomized rather than being directed
forward, and the gas cloud lacks the characteristics which would
allow it to push through solid armour rather than simply heating its
surface. And after all that, the plasmoid won't move in a straight
line the way they're invariably shown in sci-fi; it should arc
downward in gravity, just like the 30mm auto-cannon shots from the
Russian BTR-80/A in this
clip.

OK, what about plasma weapons in space?

The problems associated with trying to push a self-contained blob
of plasma through atmosphere would be greatly lessened in space for
obvious reasons, but the energy requirement also ratchets up
significantly. Plasma weapons in sci-fi are normally described to
have yields in the range of kilotons, megatons, or even higher. They
need such yields, in order to compete with guided nuclear-tipped
missiles over which they suffer from substantially increased
technological difficulties and few if any advantages.

Let us examine a hypothetical plasmoid
with a yield of 1 megaton and an approximate volume of 1 million
cubic metres (which is quite huge for a plasma blast, being
comparable to the volume of a small starship). If we assume we're
using hydrogen plasma with average particle energy of 100 keV (an
absurdly high temperature of nearly eight hundred million
Kelvin), you would need 2.6E29 ions (roughly 215 kg) to get 1 megaton
yield (4.2E15 J). Using the ideal gas law, the pressure in this huge
1 million m³ blob would be roughly 3 GPa, or more than three
times the yield strength of high-grade steel.

In short, the problems of the atmospheric plasma weapon are only
slightly alleviated by being in space. You still need a fantastically
strong forcefield to hold the bolt together (a requirement which
grows ever more severe with increasingly powerful plasma weapons),
you still have the question of why the enemy doesn't use a similar
forcefield to ward it off upon impact if such forcefields can be
created so easily that you can let fly with one and it will hold
itself together with no technological apparatus to sustain it, you
still have the problem that the blob's particle velocities are
randomized relative to its forward movement so it has poor
penetrative qualities, and if you're close to a planet, you even have
the gravity arcing problem to deal with. Once again, these problems
could be alleviated with the use of extreme velocities, so that the
blob's expansion rate (measured in tens of km/s) is small relative to
its forward velocity, but that would not explain the slow-moving
plasma "bolts" of sci-fi.

So why do sci-fi writers use "Plasma Weapons?"

Perhaps you should ask them. My suspicion is that they do it
because it sounds neat, and because they don't know any better (one
of the ironies of the sci-fi world is that most of the modern writers
barely know enough science to graduate high school). And whether you
like it or not, that's good enough for most sci-fi writers nowadays.
If you could invent such immensely strong forcefields as to wrap a
blob of plasma so tightly that it can fly through the air like a
solid object, then why not use this fantastic forcefield to carry
something more destructive, such as a small charge of antimatter?

There is a rational way to use "plasma weapons" in
sci-fi, but that would be the "particle beam"
interpretation, not the "slowly moving discrete plasmoid"
interpretation.

What should sci-fi writers use instead of these slow-moving
plasma blobs?

Pretty much anything else, really. Guns, missiles, bombs, lasers,
and particle beams (particularly neutral-beams such as neutron
cannons, where the electromagnetic repulsion problem won't cause beam
spreading and electromagnetic shielding would be ineffective) all
work fine and don't require such fantastic rationalizations as a
magical moving self-powered self-sustained containment field which
defies gravity and is a thousand times stronger than steel, but they
are also familiar, and to a substantial portion of sci-fi
writers, familiarity breeds contempt.

Some Fun Facts about Plasma

The plasma at the surface of the Sun has a temperature of
roughly 6000K. The temperature in the core of the Sun is roughly 15
million K. The temperature in the centre of a lightning bolt is
around 50 million K. The projected temperature in the plasmoid of a
commercially viable nuclear fusion reactor would have to be well in
excess of 100 million K. Steel melts at 1810K.

Plasma glows primarily through bremsstrahlung, or
braking radiation. This is the process whereby charged particles are
scattered or deflected by interaction with other matter. When they
lose kinetic energy in the process, it is emitted as a photon. In
the presence of a powerful magnetic field, it is also possible for
synchrotron or cyclotron emission
processes to become significant, as the charged particles move about
the lines of magnetic force. Normal non-ionized matter glows through
line radiation, whereby captured electrons in higher energy
states drop to lower energy states and emit the difference as a
photon.

The particles in a typical fusion plasma rarely interact, due
to the great velocity of the particles relative to the range and
strength of electromagnetic interactions. Without some kind of
confinement, a typical ion is most likely to escape from the
plasmoid without scattering, never mind fusion. In fact, the mean
free path for 90º scattering in such a plasma is on the order
of tens of kilometres. However, plasmas can become more
collisional with extreme high-pressure confinement (for example, in
stellar cores where the pressure is so great that the plasma is
compressed to a greater density than uranium).

Plasmas closely approximate the behaviour of ideal gases,
hence they can be modeled with the ideal gas law, PV=NRT. You may
recall the ideal gas law from your high-school physics classes, but
if not, it states that the product of pressure and volume for a
gaseous body is linearly correlated to its mass and temperature.
Note that astrophysicists prefer the form P=nkT, where n is particle
density and k is the Boltzmann constant.

If a deuterium plasma achieves a sufficiently high density
and temperature, nuclear fusion will occur. For example, the 3.51GW
(gross output) STARFIRE2
(a model of the performance parameters theoretically required for a
commercially viable fusion reactor, not an actual working design)
calls for a centreline plasma density of 1.69E20 deuterons per cubic
metre (0.806E20 DT/m³ average), with a total volume of 781 m³.
Average electron and deuteron temperatures are 17.3 keV and 24.1 keV
respectively. In layman's terms, this is an average deuteron density
and temperature of 2.695E-7 kg/m³ and 186 million K
respectively. In other words, the STARFIRE's plasmoid would fill a
volume greater than that of a one thousand square foot apartment
with just 0.0002 kg of plasma, despite a confinement pressure
in excess of 200 kPA. However, these requirements, as difficult as
they may seem, actually exaggerate the real likelihood of fusion in
a plasmoid because they are based on a high-purity D-T plasma. The
ignition temperature for D-D fusion is a full order of magnitude
higher than that for D-T fusion, and the requirements for H-H fusion
are far higher still.

Electrically powered plasma torches also exist in real-life,
some of which actually extend into the megawatt range. However,
their energy density is limited by the density of plasma itself, and
they have proven suitable for melting solids, but not vapourizing
them. Hence the “fusion torch” concept proposed by
Eastland and Gough, in which plasma is exhausted directly from a
fusion reactor. But in either case, they are extremely short-ranged
because of the dispersion problem.

The reaction cross-section for coulomb scattering at 10 keV
is on the order of 1E4 barns, while the reaction cross-section for
D-T fusion at the same energy level is on the order of 1E-2 barns,
ie- a million times smaller than the reaction cross-section
for scattering3.
And the reaction cross-section for D-D fusion at that energy level
is two orders of magnitude smaller still! In other words, even
though a deuterium ion in a typical 10 keV plasma is likely to
travel for several kilometres without Coulomb scattering,
that is still a hundred million times more likely than fusion
with another deuterium ion.

Related Links

FinePlasma.org: a
manufacturer website for plasma cutting machines. The specifications
can be quite interesting; for example, one of their machines can cut
½" thick mild steel plate at a rate of 100 ipm and a
cutting width of 0.03" using an 8.5kVA plasma generator. A few
simple calculations lead to the conclusion that an 8.5kVA plasma
cutter can eliminate mild steel at a rate of ~0.4cm³/s.

BBC News
article on the use of "plasma bullets" for ocular
microsurgery (obviously a very short-ranged application).

Janes
Defense Weekly article on plasma-based weapons (note that it
largely discusses the use of hypersonic aircraft plasmas as a lasing
medium rather than traditional sci-fi "plasma bullets") and
it also touches on the discontinued "Shiva Star"
high-velocity plasma project, which aimed to solve the range problem
with extreme velocities on the order of as much as 10,000
km/s.

Introducing
the Particle-Beam Weapon: an article written by Dr. Richard
Roberds on the feasibility of particle-beam weapons (not the same as
traditional sci-fi "plasma bullets", but nonetheless
interesting as an exploration of where one can go with particle beams
or ion cannons). Note that the atmospheric-ionization pinch-current
confinement mechanism described in the article for charged-particle
beams can only delay the beam's dissolution rather than preventing it
unless the beam is rendered charge-neutral, and it does not
apply to a self-contained discrete plasmoid; it requires a continuous
high-velocity stream.

Acknowledgements

Curtis Saxton, for general discussion as well as useful
suggestions and corrections.